Width Minimization O n reconfigurable Single-Electron Transistor Arrays

1. Width Minimization On reconfigurable Single-Electron Transistor Arrays Speaker: Chain Wei Liu Advisor: Dr. Chun-Yao Wang 2013/06/03

2. OUTLINE • Introduction • Width minimization approach • Problem • Future work

3. Introduction current detector • SET: Single-Electron Transistor • An SET array can be presented as a graph composed of hexagons 1

4. Example • An example of a XOR b: • ab’+ba’ active high a active low short • All sloping edges areconfigurable • short, open, active (high or low) • Active edges at the same row are controlled by a single variable open b

5. Mapping constraint • Granularity constraint • Two edges are configured simultaneously • The combination of n.left and n.right, (n.left,n.right), must be one of (high, low), (low, high), (short, short),and (open, open), where n is a node in the SET array. • Fabric constraint • (high, low) and (low, high) cannot simultaneously appear in a row

6. OUTLINE • Introduction • Width minimization approach • Problem • Future work

7. Key idea • Relax mapping constraint • More Branch-and Share can be used • Limiting expansion of the SET array • In the previous work, for simplification, they allow only one of (high, low) and (low, high) to appear in an SET array • For width minimization, we allow both (high, low) and (low, high) to appear in an SET array

8. Width optimization approach

9. Share collection

10. Example-share collection 110100 P1 1100-- P2 1111-- P3 111000 P4 11101- P5 110100 P1 1100-- P2 1111-- P3 111000 P4 11101- P5 110100 P1 1100-- P2 1111-- P3 111000 P4 11101- P5 Share collection

11. Determine the SET array architecture • The first row is always configured as (high,low) • When there is a Branch-and-share, determine the row structure to meet the Branch-and-share requirement • Other row structures are determined as the previous row structure if over half of variables changes their value • Otherwise, inverse the row structure

12. Example-determine architecture H,L L,H H,L L,H L,H H,L 110100 P1 1100-- P2 1111-- P3 111000 P4 11101- P5

13. Product term order determination • Determine the product term order by expansion level, share collection and group relation • Priority: share collection > group relation > expansion level

14. Example-product term reordering H,L L,H H,L L,H L,H H,L 110100 P1 1100-- P2 1111-- P3 111000 P4 11101- P5 P1~P5 111 110 P3~P5 1110 1111 P1 P2 110100 P1 110011 P2 111111 P3 111000 P4 111011 P5 P1: 4 P2: 3 P3: 3 P4: 4 P5: 5 P4 P5 P2->P3->P5->P4->P1 P3

15. Example-mapping result Previous work Width optimization approach Width=13 Width=9

16. OUTLINE • Introduction • Width minimization approach • Problem • Future work

17. Problem • The previous product term function will cause SET array be Nonequivalence in some benchmarks • The product term ordering may destroy the consecutive Branch-and-Share relationship • The configure function may destroy the Branch-and –Share relationship • To get better result, we may need to backtrack while configuring

18. Width optimization approach

19. Width optimization approach • Configure • Relax configuring constraint • Backtrack • Allow reconfigure product terms

20. OUTLINE • Introduction • Width minimization approach • Problem • Future work

21. Future Work • Solve above problems